Nonlinear inversion of potential field data has been traditionally accomplished by the least squares method. As far as the anomalous field is corrupted by Gaussian random noise. Least squares inversion has a good performance. However, when the data are contaminated by non Gaussian noise, which is the case of most geological noise, the least squares method presents an extremely poor performance. As a result, alternative methods must be employed in this case in order to produce realistic and meaningful interpretations. This paper presents a comparison among the least squares method, the minimum absolute error and M-fitting applied to non linear inversion of potential field data. The analysis is performed using theoretical data generated by synthetic models simulating several geological settings. The results show that in the presence of geological noise represented either by small shallow bodies above the main body, or by large interfering bodies adjacent to the main body, M-fitting presents a much batter performance as compared with the least squares or the minimun absolute error methods. In the presence of Gaussian random noise, however M-fitting has a poor performance. Since a Gaussian noise is a white noise, a law pass filter applied to the observed data would remove part of the Gaussian noise with a minimum loss of the low wavenumber signal. On the other hand, most geological noise have important low wavenumber spectral components so that this noise cannot be eliminated without a significant loss of signal. Therefore, the M-fitting method may become an important interpretation tool when applied to complex areas (where anomalies are usually contaminated by geological noise) provided the data have been previously filtered by a suitable law pass filter. All three methods analysed in the paper are applied to a real magnetic anomaly due to a dike of diabasic rock intruded in sandstones and shales from the Piauí Formation, in Parnaíba Basin, Brazil. All three methods yielded similar interpretations which are consistent with the available a priori geological information. The fact that all methods produced similar results indicates a low level of geological and Gaussian random noise in the data.
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